Respiratory Bacteria Vaccines: Model Analyses for Vaccine and Vaccine Trial Design

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Respiratory Bacteria Vaccines Model Analyses
for Vaccine and Vaccine Trial Design

• Jim Koopman MD MPH
• Ximin Lin MD MPH
• Tom Riggs MD MPH
• Dept. of Epidemiology
• Center for Study of Complex Systems
• University of Michigan

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Questions Addressed

• What role does immunity affecting pathogenicity
  vs. transmission play in the sharp drop with age
  in NTHi otitis media?
• What vaccine effects should be sought and
  measured in trials?
• How should vaccine trials be designed to insure
  adequate power to detect important effects?

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General Issues Regarding NTHi

• Causes 20-40 of acute otitis media
• Vaccine market 1 billion per year in U.S.
• Infection, immunity, and disease data is meager,
  non-specific, highly variable
• Knowledge of natural history of infection and
  immunity is deficient
• Unquestioned assumption that vaccine trials will
  be individual based and assess disease outcomes

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Aspects of NTHi ( many other bacterial)
infections

• Partial immunity, rarely sterilizing
• IgA proteases show evolutionary importance of
  immunity
• Many variants arise due to transformation
  competency
• No permanent strains yet identified
• Immunity to colonization or infection, disease,
  transmission can be distinct

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Using NTHi Models for Inference

• Models with diverse natural Hx of infection and
  immunity, age groupings, and contact patterns
  were constructed
• Deterministic compartmental (DC) models built
  first
• Gradual acquisition of immunity with each
  colonization and continuous loss over time
• All models were fit to the full range of data
  conformations deemed plausible using least
  squares
• Projections of vaccine effects made for all fits
  of all models (about 1000 total)
• Individual event history stochastic models
  corresponding to the DC models were used for
  vaccine trial design

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Natural history of NTHi colonization
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FA model
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Modeling partial immunity

• Model agent variation and host response as
  single process
• Assumptions
• equal immunity from each colonization
• multiplicative effects of sequential infections
• immunity limit (m levels)
• immunity waning

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Modeling partial immunityS1I1S2I2S3I3Sm-1Im-1
SmIm vs. SIR/SIRS/SIS
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Aspects of Immunity Modeled

• Susceptibility
• Contagiousness
• Pathogenicity
• Duration

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Population structure

• Preschool children (0.5-5 years)
• Day-care Non-day-care
• 9 age groups with 6-month interval
• School children (5-15 years)
• Adults

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Population structure
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Contact structure
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Population parameters
Death rate of individuals less than 1 year 0.00181
Death rate of individuals aged 1-2 years 0.00036
Death rate of individuals aged 3-4 years 0.00036
Death rate of individuals aged 5-15 years 0.00021
Death rate of individuals aged 15 years and over 0.01086
Annual birth rate into 7-12 month age group 0.00938
Rate at which children enter daycare 0.174
Rate at which children leave daycare 0.0358
Day-care attendance at 6 months 0.0785
The units of all rates are year-1.
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Limited Highly Variable Epidemiologic data

• NTHi prevalence by age daycare attendance
  (diverse methods)
• AOM incidence lt age 5 by daycare (combine
  incidence studies fraction with NTHi studies)
• Antibody levels by age (diverse methods)
• Colonization duration (quite limited)
• Daycare risk ratios for AOM

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Other Data

• Antibody levels peak during elementary school
• Daycare Risk Ratios from 2 to 3
• Colonization mean of 2 months but many transient
  episodes and some long (limited data)
• Waning seems to be relatively fast

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Presumptions Before Our Work

• Very different from Hi Type B
• Colonization is so frequent, even at older ages,
  that immunity to transmission cannot be important
• Trials should assess effects on AOM, not
  colonization

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General assumptions of our model

• Every colonized individual is infectious
• Acute otitis media (AOM) is the only relevant
  disease (Unlike Hi Type B or Strep pneumo)
• Maternal immunity (Children aged 0-6 months
  totally immune from colonization)

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Fitting model to epidemiologic data

• Berkeley Madonna boundary value ODE
  optimize functions
• Empirical identifiability checking
• Extensive robustness assessment for both data
  conformation and model conformation rather than
  estimating variance of estimates

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Fitting Results

• Most efficient level is 4
• Needed immunity profile includes
• Susceptibility
• Contagiousness
• Pathogenicity
• Contagiousness and Duration Effects are highly
  co-linear when fitting equilibrium

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Parameter values that fit NTHi prevalence AOM
incidence for models without all immunity effects.
Immune Effects In The Model (Path effects in all models) Immune Effects In The Model (Path effects in all models) Immune Effects In The Model (Path effects in all models) Immune Effects In The Model (Path effects in all models)
Susc S Infect S Durat D I
Goodness of Fit (Root Mean Square Error) 0.01 0.02 0.03 0.37
Duration of immunity (years) 1/w 84.7 9.8 4.0 5.1
Relative susceptibility after each colonization q 0.55 0.519 0.535 1
Relative contagiousness when re-infected c 1 0.76 1 0.301
Relative duration of colonization when re-infected d 1 1 0.839 0.599
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Colonization prevalence and AOM incidence data fit Colonization prevalence and AOM incidence data fit Colonization prevalence and AOM incidence data fit Colonization prevalence and AOM incidence data fit
H col H AOM H col L AOM L col H AOM L col L AOM
Goodness of fit (root mean square error) 0.07 0.05 0.05 0.02
Duration of each level of immunity (years), 3.7 4.7 3.4 9.8
Duration / stage colonization lowest immunity 0.104 0.107 0.0613 0.0549
P(AOM colonization at the lowest immunity) 0.343 0.127 0.374 0.136
decrease in AOM probability per immunity level (pathogenicity effect), 0.334 0.301 0.294 0.279
decrease in susceptibility per immunity level, 0.597 0.594 0.732 0.481
decrease in contagiousness / immunity level, 0.582 0.237 0.116 0.24
Effective contact rate per year at general site, 173 80.1 50.3 94.4
Effective contact rate per year at daycare site, 655 218 359 113
Effective contact rate per year at school site, 301 68 217 61
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Sensitivity Analysis to 10 Change In
Pathogenicity or Transmission Immunity
Data Conformation Fitted Data Conformation Fitted AOM Incidence Decrease AOM Incidence Decrease AOM Incidence Decrease AOM Incidence Decrease AOM Incidence Decrease
Colon-ization Prev-alence AOM Inci-dence Immunity Type Decreased 0-1 year 1-2 years 2-3 years 3-4 years 4-5 years
High High Pathogenicity 1.6 3.9 7.9 10.9 12.5
High High Transmission 12.0 9.5 11.8 17.8 23.4
High Low Pathogenicity 1.6 3.8 7.6 10.2 13.2
High Low Transmission 23.4 14.6 15.3 23.6 32.8
Low High Pathogenicity 1.4 2.9 5.1 6.8 8.1
Low High Transmission 15.9 19.2 32.6 48.7 62.7
Low Low Pathogenicity 1.8 3.7 6.7 9.0 10.4
Low Low Transmission 59.7 34.1 33.5 53.2 70.3
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Age 0-1
Age 1-2
Age 2-3
Age 3-4
Age 4-5
Further Sensitivity Analysis
Base analysis from previous Table 16.5 5.5 3.7 4.2 4.8
Only susceptibility effects on transmission 15.6 6.0 3.9 4.3 4.7
Susceptibility and duration effects on transmission 8.4 2.6 1.4 1.5 1.8
Susceptibility, contagiousness, duration effects on transmission 10.2 3.3 2.1 2.5 2.8
Eight levels of immunity 4.6 5.1 2.0 1.5 1.7
Alternate ratios of contact rates by age at the general mixing site 39.5 11.0 5.9 6.7 7.6
Prevalence and incidence fall more steeply with age 19.2 4.7 0.6 0.6 1.2
Prevalence and incidence fall less steeply with age 9.5 3.3 2.0 2.0 2.0
Simpler pattern of compartments for the natural history of infection and immunity 36.3 6.4 3.2 3.4 3.9
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Immunity acquisition waning for P vaccine
(Vaccine effects dont exceed natural immunity
effects)
Vaccination
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Immunity acquiring waning in vaccinated
population SIP vaccine
Vaccination
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Vaccination strategy

• All children at age of 6 months vaccinated

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reduction in AOM incidence among all preschool
children as the result of vaccination at birth
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reduction in AOM incidence among preschool
children due to vaccination at birth.
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Absolute reduction of AOM incidence by age and
daycare attendance among preschool children due
to vaccination at birth.
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AOM cases among daycare and non-daycare children
from a population of 1,000,000 before and after
vaccination at birth with SIP vaccines.
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Summary of Deterministic Model Findings

• Wide range of feasible models fit to a wide range
  of feasible data
• Over this entire huge range, the intuition that
  immune effects on pathogenicity are the major
  determinants of AOM incidence proves to be wrong
• Trials must assess transmission

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Model Refinements Desirable

• Model agent strains with different degrees of
  cross reacting immunity
• Incorporate evolution of agent into vaccine
  effect assessment
• Make maternal immunity and acquisition time for
  vaccine immunity more realistic

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Additional Practical Need for Indirect Effects

• Very young age of highest risk means little time
  to get all the booster effects needed

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Using NTHi Models for Inference About Vaccine
Trial Design

• Convert deterministic compartmental model to
  individual event history model
• Add distinct daycare units and families
• Construct vaccine trials assessing colonization
  in the IEH models with varying randomization
  schemes, vaccine effects exceeding natural
  immunity, sample collection periods, serology
  typing results
• Hundreds of thousands of vaccine trial
  simulations performed

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Conclusions from Vaccine Trial Simulations

• Most efficient randomization unit is daycare
• Individual randomized trials run too much risk of
  missing important vaccine effects
• Standard power calculation methods for Group
  Randomized Trials are far off because they are
  based on individual effect
• Role of inside vs. outside transmission in
  daycare significantly affects power
• Molecular assessment of transmission worthwhile

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Standard variance calculation in Group Randomized
Trials (GRTs)

• variance
• ICC intraclass correlation
• Assumes objective is measurement of individual
  effects

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ICC Vaccine effect
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Change in Variance with Daycare Size Sample Size
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Preliminary results (1) variance immunity
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Simple Model For Insight
S
I
S
Equilibrium distribution of states solved
theoretically for daycare with 12
children Vaccine effect decreases susceptibility
by 50
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Unvacc mostly within trans 30Prev
Unvacc mostly outside trans
Vacc mostly within trans
Vacc mostly outside trans
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Unvacc mostly within trans 50Prev
Unvacc mostly outside trans
Vacc mostly within trans
Vacc mostly outside trans
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Significance of S S Contribution to Power
Calculation

• Serological ability to assess cumulative
  infection level would contribute considerably to
  power

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Empirical power calculation
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Empirical power the number of the pairs of
daycare centers
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Why standard power calculations for GRTs are way
off

• ICC is determined by transmission dynamics
• Effect is determined by transmission dynamics
• Power is not just determined a single outcome
  state but by correlated infection and immunity
  states

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Thank You